Computation of Total Vertex Irregularity Strength of Theta Graphs
A total labeling <inline-formula> <tex-math notation="LaTeX">$\phi: V(G)\cup E(G) \to \{1,2, {\dots }, k\}$ </tex-math></inline-formula> is called a <italic>vertex irregular total</italic> <inline-formula> <tex-math notation="LaTeX">...
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IEEE
2019-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8786105/ |
| _version_ | 1818479901300228096 |
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| author | Ali N. A. Koam Ali Ahmad |
| author_facet | Ali N. A. Koam Ali Ahmad |
| author_sort | Ali N. A. Koam |
| collection | DOAJ |
| description | A total labeling <inline-formula> <tex-math notation="LaTeX">$\phi: V(G)\cup E(G) \to \{1,2, {\dots }, k\}$ </tex-math></inline-formula> is called a <italic>vertex irregular total</italic> <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula><italic>-labeling</italic> of a graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> if different vertices in <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> have different weights. The weight of a vertex is defined as the sum of the labels of its incident edges and the label of that vertex. The minimum <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> for which the graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> has a vertex irregular total <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-labeling is called the <italic>total vertex irregularity strength</italic> of <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>, denoted by <inline-formula> <tex-math notation="LaTeX">$tvs(G)$ </tex-math></inline-formula>. In this paper we deal with the total vertex irregularity strength of uniform theta graphs and centralized uniform theta graphs. Theta graph is a closer representation of bipolar electric or magnetic fields so labeling of various theta graphs can help the law of physics in future. |
| first_indexed | 2024-12-10T11:16:13Z |
| format | Article |
| id | doaj.art-942b276c9d914ea798c349235ac427af |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-10T11:16:13Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
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| series | IEEE Access |
| spelling | doaj.art-942b276c9d914ea798c349235ac427af2022-12-22T01:51:09ZengIEEEIEEE Access2169-35362019-01-01711382611383110.1109/ACCESS.2019.29326758786105Computation of Total Vertex Irregularity Strength of Theta GraphsAli N. A. Koam0Ali Ahmad1https://orcid.org/0000-0003-3434-9908Department of Mathematics, College of Science, Jazan University, Jazan, Saudi ArabiaCollege of Computer Science and Information Technology, Jazan University, Jazan, Saudi ArabiaA total labeling <inline-formula> <tex-math notation="LaTeX">$\phi: V(G)\cup E(G) \to \{1,2, {\dots }, k\}$ </tex-math></inline-formula> is called a <italic>vertex irregular total</italic> <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula><italic>-labeling</italic> of a graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> if different vertices in <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> have different weights. The weight of a vertex is defined as the sum of the labels of its incident edges and the label of that vertex. The minimum <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> for which the graph <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula> has a vertex irregular total <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-labeling is called the <italic>total vertex irregularity strength</italic> of <inline-formula> <tex-math notation="LaTeX">$G$ </tex-math></inline-formula>, denoted by <inline-formula> <tex-math notation="LaTeX">$tvs(G)$ </tex-math></inline-formula>. In this paper we deal with the total vertex irregularity strength of uniform theta graphs and centralized uniform theta graphs. Theta graph is a closer representation of bipolar electric or magnetic fields so labeling of various theta graphs can help the law of physics in future.https://ieeexplore.ieee.org/document/8786105/Total vertex irregularity strengththeta graphscentralized uniform theta graphs |
| spellingShingle | Ali N. A. Koam Ali Ahmad Computation of Total Vertex Irregularity Strength of Theta Graphs IEEE Access Total vertex irregularity strength theta graphs centralized uniform theta graphs |
| title | Computation of Total Vertex Irregularity Strength of Theta Graphs |
| title_full | Computation of Total Vertex Irregularity Strength of Theta Graphs |
| title_fullStr | Computation of Total Vertex Irregularity Strength of Theta Graphs |
| title_full_unstemmed | Computation of Total Vertex Irregularity Strength of Theta Graphs |
| title_short | Computation of Total Vertex Irregularity Strength of Theta Graphs |
| title_sort | computation of total vertex irregularity strength of theta graphs |
| topic | Total vertex irregularity strength theta graphs centralized uniform theta graphs |
| url | https://ieeexplore.ieee.org/document/8786105/ |
| work_keys_str_mv | AT alinakoam computationoftotalvertexirregularitystrengthofthetagraphs AT aliahmad computationoftotalvertexirregularitystrengthofthetagraphs |